Finite Group Databasebeta

← C103×#29245 #39934520

Subgroups — C103×#29245 #39934520

Order 26368.

770 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C22⋊Q8×C103C211yesmaximal, characteristic
2C103×#2296C211yesmaximal, characteristic
3C103×#2088C211yesmaximal, characteristic, complemented
4C103×#2087C211yesmaximal, characteristic, complemented
5C103×#2068C211yesmaximal, characteristic, complemented
6C103×#2066C211yesmaximal, characteristic, complemented
7C103×#1920C211yesmaximal, characteristic, complemented
8C103×#1918C211yesmaximal, characteristic, complemented
9C103×#1873C211yesmaximal, characteristic
10C103×#1873C211yesmaximal, characteristic
11C103×#1865C211yesmaximal, characteristic, complemented
12C103×#1863C211yesmaximal, characteristic, complemented
13C103×#1854C211yesmaximal, characteristic
14C103×#1854C211yesmaximal, characteristic
15C103×#1797C211yesmaximal, characteristic
16C2×C22⋊Q8×C103C2211yescharacteristic
17C2×C4×Q8×C103C2211yescharacteristic
18C2×#117×C103C2211yescharacteristic
19C2×#117×C103C2211yescharacteristic
20C22×C42×C103C2211yescharacteristic
21C2×#107×C103C2211yescharacteristic
22C2×#107×C103C2211yescharacteristic
23C2×#106×C103C2211yescharacteristic
24C2×#106×C103C2211yescharacteristic
25C2×C4⋊C8×C103C2211yescharacteristic
26C2×C4⋊C8×C103C2211yescharacteristic
27C2×#103×C103C2211yescharacteristic
28C2×#103×C103C2211yescharacteristic
29C2×#103×C103C2211yescharacteristic
30C2×#103×C103C2211yescharacteristic
31C2×C22⋊C8×C103C2211yescharacteristic
32C2×C22⋊C8×C103C2211yescharacteristic
33#391×C103C2211yescharacteristic
34#389×C103C2211yescharacteristic
35#389×C103C2211yescharacteristic
36#389×C103C2211yescharacteristic
37#389×C103C2211yescharacteristic
38#389×C103C2211yescharacteristic
39#387×C103—21no—
40#385×C103—21no—
41#385×C103—21no—
42#385×C103—21no—
43#380×C103C2211yescharacteristic
44C4×C4⋊C4×C103—21no—
45C4×C4⋊C4×C103—21no—
46C4×C4⋊C4×C103—21no—
47C4×C4⋊C4×C103C2211yescharacteristic
48C4×C22⋊C4×C103—21no—
49#340×C103C2211yescharacteristic
50#340×C103C2211yescharacteristic
51#340×C103C2211yescharacteristic
52#340×C103C2211yescharacteristic
53#340×C103C2211yescharacteristic
54#340×C103C2211yescharacteristic
55#340×C103C2211yescharacteristic
56#340×C103C2211yescharacteristic
57#336×C103C2211yescharacteristic
58#336×C103C2211yescharacteristic
59C22×Q8×C103C2311yescharacteristic
60C23×C4×C103D411yescharacteristic
61C23×C4×C103D411yescharacteristic
62C23×C4×C103C2311yescharacteristic
63C22×C8×C103C2311yescharacteristic
64C22×C8×C103C2311yescharacteristic
65C22×C8×C103C2311yescharacteristic
66C22×C8×C103C2311yescharacteristic
67C22⋊Q8×C103—22no—
68C22⋊Q8×C103Q814yes—
69C4×Q8×C103—41no—
70C4×Q8×C103—41no—
71#117×C103—22no—
72#117×C103—22no—
73#117×C103—41no—
74#117×C103—41no—
75C2×C4⋊C4×C103—21no—
76C2×C4⋊C4×C103—21no—
77C2×C4⋊C4×C103—21no—
78C2×C4⋊C4×C103—21no—
79C2×C4⋊C4×C103—21no—
80C2×C4⋊C4×C103—21no—
81C2×C4⋊C4×C103—21no—
82C2×C4⋊C4×C103C2311yescharacteristic
83C2×C4⋊C4×C103C2311yescharacteristic
84C2×C4⋊C4×C103C2311yescharacteristic
85C2×C4⋊C4×C103C2311yescharacteristic
86C2×C4⋊C4×C103C2311yescharacteristic
87C2×C4⋊C4×C103C2311yescharacteristic
88C2×C4⋊C4×C103C2311yescharacteristic
89C2×C22⋊C4×C103—21no—
90C2×C22⋊C4×C103—21no—
91C2×C22⋊C4×C103—21no—
92C2×C22⋊C4×C103—21no—
93C2×C42×C103—21no—
94C2×C42×C103—21no—
95C2×C42×C103—21no—
96C2×C42×C103—21no—
97C2×C42×C103—41no—
98C2×C42×C103—41no—
99C2×C42×C103D411yescharacteristic
100C2×C42×C103D411yescharacteristic
101C2×C42×C103C2311yescharacteristic
102C2×C42×C103C2311yescharacteristic
103#107×C103—22no—
104#107×C103—41no—
105#106×C103—22no—
106#106×C103—41no—
107C4⋊C8×C103—41no—
108C4⋊C8×C103—41no—
109#103×C103—22no—
110#103×C103—22no—
111#103×C103—41no—
112#103×C103—41no—
113C22⋊C8×C103—22no—
114C22⋊C8×C103—22no—
115#95×C103—21no—
116#95×C103—21no—
117#95×C103—21no—
118#95×C103—21no—
119#95×C103—21no—
120#95×C103—21no—
121#95×C103—21no—
122#95×C103—21no—
123#95×C103—21no—
124C24×C103C2×D411yescharacteristic
125C2×Q8×C103—21no—
126C2×Q8×C103—21no—
127C2×Q8×C103—21no—
128C2×Q8×C103—21no—
129C2×Q8×C103—21no—
130C2×Q8×C103C2×Q812yes—
131C22×C4×C103—21no—
132C22×C4×C103—21no—
133C22×C4×C103—21no—
134C22×C4×C103—21no—
135C22×C4×C103—21no—
136C22×C4×C103—21no—
137C22×C4×C103—21no—
138C22×C4×C103—21no—
139C22×C4×C103—22no—
140C22×C4×C103—22no—
141C22×C4×C103—21no—
142C22×C4×C103—21no—
143C22×C4×C103—21no—
144C22×C4×C103—21no—
145C22×C4×C103—41no—
146C22×C4×C103—41no—
147C22×C4×C103—41no—
148C22×C4×C103—41no—
149C22×C4×C103C2×D411yescharacteristic
150C22×C4×C103C2×D411yescharacteristic
151C22×C4×C103C2×D411yescharacteristic
152C22×C4×C103C2×D411yescharacteristic
153C22×C4×C103C2×D411yescharacteristic
154C22×C4×C103C2×Q812yes—
155C22×C4×C103#4112yes—
156C22×C4×C103C2411yescharacteristic
157C2×C8×C103—21no—
158C2×C8×C103—21no—
159C2×C8×C103—21no—
160C2×C8×C103—21no—
161C2×C8×C103—21no—
162C2×C8×C103—21no—
163C2×C8×C103—21no—
164C2×C8×C103—21no—
165C2×C8×C103—21no—
166C2×C8×C103—21no—
167C2×C8×C103—21no—
168C2×C8×C103—21no—
169C4⋊C4×C103—24no—
170C4⋊C4×C103—21no—
171C4⋊C4×C103—21no—
172C4⋊C4×C103—21no—
173C4⋊C4×C103—21no—
174C4⋊C4×C103—21no—
175C4⋊C4×C103—21no—
176C4⋊C4×C103—21no—
177C4⋊C4×C103—21no—
178C4⋊C4×C103—21no—
179C4⋊C4×C103—21no—
180C4⋊C4×C103—21no—
181C4⋊C4×C103—42no—
182C4⋊C4×C103—42no—
183C4⋊C4×C103—42no—
184C4⋊C4×C103—42no—
185C4⋊C4×C103—42no—
186C4⋊C4×C103—42no—
187C4⋊C4×C103C2×Q812yes—
188C4⋊C4×C103#4112yes—
189C4⋊C4×C103#4112yes—
190C22⋊C4×C103—24no—
191C22⋊C4×C103—24no—
192C22⋊C4×C103—42no—
193C22⋊C4×C103—42no—
194C42×C103—24no—
195C42×C103—21no—
196C42×C103—21no—
197C42×C103—21no—
198C42×C103—21no—
199C42×C103—41no—
200C42×C103—41no—
201C42×C103—42no—
202C42×C103—42no—
203C42×C103—42no—
204C23×C103—21no—
205C23×C103—21no—
206C23×C103—21no—
207C23×C103—21no—
208C23×C103—21no—
209C23×C103—21no—
210C23×C103C22⋊Q812yes—
211C23×C103C22×D411yescharacteristic
212Q8×C103—22no—
213Q8×C103—22no—
214Q8×C103—41no—
215Q8×C103—41no—
216C2×C4×C103—21no—
217C2×C4×C103—21no—
218C2×C4×C103—21no—
219C2×C4×C103—21no—
220C2×C4×C103—21no—
221C2×C4×C103—21no—
222C2×C4×C103—22no—
223C2×C4×C103—22no—
224C2×C4×C103—22no—
225C2×C4×C103—22no—
226C2×C4×C103—22no—
227C2×C4×C103—22no—
228C2×C4×C103—22no—
229C2×C4×C103—22no—
230C2×C4×C103—21no—
231C2×C4×C103—21no—
232C2×C4×C103—21no—
233C2×C4×C103—21no—
234C2×C4×C103—21no—
235C2×C4×C103—21no—
236C2×C4×C103—44no—
237C2×C4×C103—44no—
238C2×C4×C103—41no—
239C2×C4×C103—41no—
240C2×C4×C103—41no—
241C2×C4×C103—41no—
242C2×C4×C103—41no—
243C2×C4×C103—41no—
244C2×C4×C103—41no—
245C2×C4×C103—41no—
246C2×C4×C103—41no—
247C2×C4×C103—41no—
248C2×C4×C103—41no—
249C2×C4×C103—41no—
250C2×C4×C103—41no—
251C2×C4×C103—41no—
252C2×C4×C103—41no—
253C2×C4×C103—41no—
254C2×C4×C103—41no—
255C2×C4×C103—41no—
256C2×C4×C103—41no—
257C2×C4×C103—41no—
258C2×C4×C103C22⋊Q812yes—
259C2×C4×C103#13512yes—
260C2×C4×C103#13712yes—
261C2×C4×C103C22×Q811yescharacteristic
262C2×C4×C103C2×#4111yescharacteristic
263C2×C4×C103C2×#4111yescharacteristic
264C2×C4×C103C2×#4111yescharacteristic
265C2×C4×C103H(5,𝔽2)11yescharacteristic
266C2×C4×C103H(5,𝔽2)11yescharacteristic
267C8×C103—41no—
268C8×C103—41no—
269C8×C103—41no—
270C8×C103—41no—
271C22×C103—22no—
272C22×C103—22no—
273C22×C103—22no—
274C22×C103—41no—
275C22×C103—41no—
276C22×C103—41no—
277C22×C103—41no—
278C22×C103C2×C22⋊Q811yescharacteristic
279C22×C103#52511yescharacteristic
280C22×C103#53411yescharacteristic
281C22×C103C2×#13511yescharacteristic
282C22×C103C2×#13711yescharacteristic
283C22×C103#57511yescharacteristic
284C22×C103#57511yescharacteristic
285C4×C103—22no—
286C4×C103—22no—
287C4×C103—22no—
288C4×C103—42no—
289C4×C103—42no—
290C4×C103—42no—
291C4×C103—42no—
292C4×C103—41no—
293C4×C103—41no—
294C4×C103—81no—
295C4×C103—81no—
296C4×C103—81no—
297C4×C103—81no—
298C4×C103#55311yescharacteristic
299C4×C103#55311yescharacteristic
300C4×C103#55411yescharacteristic
301C4×C103#55411yescharacteristic
302#29245C10311yesmaximal, characteristic, direct product factor, Sylow
303C2×C103—42no—
304C2×C103#257911yescharacteristic
305C2×C103#307611yescharacteristic
306C2×C103#307811yescharacteristic
307C2×C103#310211yescharacteristic
308C2×C103#311611yescharacteristic
309C2×C103#319011yescharacteristic
310C2×C103#319711yescharacteristic
311C4×C22⋊Q8C2×C10311yescharacteristic
312#2296C2×C10311yescharacteristic
313#2088C2×C10311yescharacteristic, complemented
314#2087C2×C10311yescharacteristic, complemented
315#2068C2×C10311yescharacteristic, complemented
316#2066C2×C10311yescharacteristic, complemented
317#1920C2×C10311yescharacteristic, complemented
318#1918C2×C10311yescharacteristic, complemented
319#1873C2×C10311yescharacteristic
320#1873C2×C10311yescharacteristic
321#1865C2×C10311yescharacteristic, complemented
322#1863C2×C10311yescharacteristic, complemented
323#1854C2×C10311yescharacteristic
324#1854C2×C10311yescharacteristic
325#1797C2×C10311yescharacteristic
326C103#2924511yescharacteristic, direct product factor, Sylow
327C2×C22⋊Q8C22×C10311yescharacteristic
328C2×C4×Q8C22×C10311yescharacteristic
329C2×#117C22×C10311yescharacteristic
330C2×#117C22×C10311yescharacteristic
331C22×C42C22×C10311yescharacteristic
332C2×#107C22×C10311yescharacteristic
333C2×#107C22×C10311yescharacteristic
334C2×#106C22×C10311yescharacteristic
335C2×#106C22×C10311yescharacteristic
336C2×C4⋊C8C22×C10311yescharacteristic
337C2×C4⋊C8C22×C10311yescharacteristic
338C2×#103C22×C10311yescharacteristic
339C2×#103C22×C10311yescharacteristic
340C2×#103C22×C10311yescharacteristic
341C2×#103C22×C10311yescharacteristic
342C2×C22⋊C8C22×C10311yescharacteristic
343C2×C22⋊C8C22×C10311yescharacteristic
344#391C22×C10311yescharacteristic
345#389C22×C10311yescharacteristic
346#389C22×C10311yescharacteristic
347#389C22×C10311yescharacteristic
348#389C22×C10311yescharacteristic
349#389C22×C10311yescharacteristic
350#387—21no—
351#385—21no—
352#385—21no—
353#385—21no—
354#380C22×C10311yescharacteristic
355C4×C4⋊C4—21no—
356C4×C4⋊C4—21no—
357C4×C4⋊C4—21no—
358C4×C4⋊C4C22×C10311yescharacteristic
359C4×C22⋊C4—21no—
360#340C22×C10311yescharacteristic
361#340C22×C10311yescharacteristic
362#340C22×C10311yescharacteristic
363#340C22×C10311yescharacteristic
364#340C22×C10311yescharacteristic
365#340C22×C10311yescharacteristic
366#340C22×C10311yescharacteristic
367#340C22×C10311yescharacteristic
368#336C22×C10311yescharacteristic
369#336C22×C10311yescharacteristic
370C22×Q8C23×C10311yescharacteristic
371C23×C4D4×C10311yescharacteristic
372C23×C4D4×C10311yescharacteristic
373C23×C4C23×C10311yescharacteristic
374C22×C8C23×C10311yescharacteristic
375C22×C8C23×C10311yescharacteristic
376C22×C8C23×C10311yescharacteristic
377C22×C8C23×C10311yescharacteristic
378C22⋊Q8—22no—
379C22⋊Q8Q8×C10314yes—
380C4×Q8—41no—
381C4×Q8—41no—
382#117—22no—
383#117—22no—
384#117—41no—
385#117—41no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4C23×C10311yescharacteristic
394C2×C4⋊C4C23×C10311yescharacteristic
395C2×C4⋊C4C23×C10311yescharacteristic
396C2×C4⋊C4C23×C10311yescharacteristic
397C2×C4⋊C4C23×C10311yescharacteristic
398C2×C4⋊C4C23×C10311yescharacteristic
399C2×C4⋊C4C23×C10311yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—41no—
409C2×C42—41no—
410C2×C42D4×C10311yescharacteristic
411C2×C42D4×C10311yescharacteristic
412C2×C42C23×C10311yescharacteristic
413C2×C42C23×C10311yescharacteristic
414#107—22no—
415#107—41no—
416#106—22no—
417#106—41no—
418C4⋊C8—41no—
419C4⋊C8—41no—
420#103—22no—
421#103—22no—
422#103—41no—
423#103—41no—
424C22⋊C8—22no—
425C22⋊C8—22no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435C24C2×D4×C10311yescharacteristic
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8C2×Q8×C10312yes—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4C2×D4×C10311yescharacteristic
461C22×C4C2×D4×C10311yescharacteristic
462C22×C4C2×D4×C10311yescharacteristic
463C22×C4C2×D4×C10311yescharacteristic
464C22×C4C2×D4×C10311yescharacteristic
465C22×C4C2×Q8×C10312yes—
466C22×C4#41×C10312yes—
467C22×C4C24×C10311yescharacteristic
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C4⋊C4—24no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—42no—
493C4⋊C4—42no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4C2×Q8×C10312yes—
499C4⋊C4#41×C10312yes—
500C4⋊C4#41×C10312yes—
501C22⋊C4—24no—
502C22⋊C4—24no—
503C22⋊C4—42no—
504C22⋊C4—42no—
505C42—24no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—41no—
511C42—41no—
512C42—42no—
513C42—42no—
514C42—42no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23C22⋊Q8×C10312yes—
522C23C22×D4×C10311yescharacteristic
523Q8—22no—
524Q8—22no—
525Q8—41no—
526Q8—41no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—44no—
548C2×C4—44no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4C22⋊Q8×C10312yes—
570C2×C4#135×C10312yes—
571C2×C4#137×C10312yes—
572C2×C4C22×Q8×C10311yescharacteristic
573C2×C4C2×#41×C10311yescharacteristic
574C2×C4C2×#41×C10311yescharacteristic
575C2×C4C2×#41×C10311yescharacteristic
576C2×C4H(5,𝔽2)×C10311yescharacteristic
577C2×C4H(5,𝔽2)×C10311yescharacteristic
578C8—41no—
579C8—41no—
580C8—41no—
581C8—41no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22C2×C22⋊Q8×C10311yescharacteristic
590C22#525×C10311yescharacteristic
591C22#534×C10311yescharacteristic
592C22C2×#135×C10311yescharacteristic
593C22C2×#137×C10311yescharacteristic
594C22#575×C10311yescharacteristic
595C22#575×C10311yescharacteristic
596C4—22no—
597C4—22no—
598C4—22no—
599C4—42no—
600C4—42no—
601C4—42no—
602C4—42no—
603C4—41no—
604C4—41no—
605C4—81no—
606C4—81no—
607C4—81no—
608C4—81no—
609C4#553×C10311yescharacteristic
610C4#553×C10311yescharacteristic
611C4#554×C10311yescharacteristic
612C4#554×C10311yescharacteristic
613C2—42no—
614C2C103×#257911yescharacteristic
615C2C103×#307611yescharacteristic
616C2C103×#307811yescharacteristic
617C2C103×#310211yescharacteristic
618C2C103×#311611yescharacteristic
619C2C103×#319011yescharacteristic
620C2C103×#319711yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC24×C103C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C22×C42×C103 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C103×#2088C2semidirect
4. C103×#2087C2semidirect
5. C103×#2068C2semidirect
6. C103×#2066C2semidirect
7. C103×#1920C2semidirect
8. C103×#1918C2semidirect
11. C103×#1865C2semidirect
12. C103×#1863C2semidirect
302. #29245C103direct (N × H)
313. #2088C2×C103semidirect
314. #2087C2×C103semidirect
315. #2068C2×C103semidirect
316. #2066C2×C103semidirect
317. #1920C2×C103semidirect
318. #1918C2×C103semidirect
321. #1865C2×C103semidirect
322. #1863C2×C103semidirect
326. C103#29245direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C4×C22⋊Q8×C1032
C103×#22962
C103×#20882
C103×#20872
C103×#20682
C103×#20662
C103×#19202
C103×#19182
C103×#18732
C103×#18652
C103×#18632
C103×#18542
C103×#17972
#29245103